Terahertz (THz) communications, with their substantial bandwidth, are essential for meeting the ultra-high data rate demands of emerging high-mobility scenarios such as vehicular-to-everything (V2X) networks. In these contexts, beamwidth adaptation has been explored to address the problem that high-mobility targets frequently move out of the narrow THz beam range. However, existing approaches cannot effectively track targets due to a lack of real-time motion awareness. Consequently, we propose a sensing-assisted beam tracking scheme with real-time beamwidth adaptation. Specifically, the base station (BS) periodically collects prior sensing information to predict the target's motion path by applying a particular motion model. Then, we build a pre-calculated codebook by optimising precoders to align the beamwidth with various predicted target paths, thereby maximising the average achievable data rates within each sensing period. Finally, the BS selects the optimal precoder from the codebook to maintain stable and continuous connectivity. Simulation results show that the proposed scheme significantly improves the rate performance and reduces outage probability compared to existing approaches under various target mobility.